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摘要:
五模式超材料由于具有各向异性的弹性模量，在声波调控和声隐身方面有重要的潜在应用，因此受到了国内外的广泛关注。本文从五模式超材料的基本概念出发，对布拉格散射型五模式超材料的声学性质、弹性及力学性质的研究进展进行详细介绍，进一步介绍了我们所研究的局域共振型五模式超材料的声学和弹性性质，并对五模式超材料的数值计算方法、加工制备和测试技术进行详细介绍。另外还对五模式超材料的目前尚未解决的科学及工程问题进行分析讨论。受到结构调控的局域共振型五模式超材料兼具各向异性弹性模量和局域共振型声子晶体低频完全声子禁带的特性，为低频声波减振降噪及低频声隐身带来新的设计思路。
Abstract:Pentamode Metamaterials (PMs) with anisotropic elastic tensor have potential applications for acoustic cloaking, so it is attracted a lot of research interest. In the review, pentamode materials and their recent progress are introduced. It includes the concept of PMs, the acoustic and elastic properties of Bragg scattering PMs and Local resonant type of PMs. The fabrications and measurement methods are also introduced. PMs perturbed structures have advantages of anisotropic elastic tensor and 3D complete acoustic bandgap, therefore they provide a way for low-frequency acoustic cloaking.
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Key words:
- acoustic wave control /
- pentamode metamaterials /
- Bragg scattering /
- local resonance
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Abstract:Pentamode metamaterials (PMs) are one of the artificial periodic materials for which the six eigenvalues of the effective elasticity tensor only take one non-zero but five zero. Hence， PMs are also called “metafluids” by making the bulk modulus B extremely large compared to the shear modulus G. PMs with anisotropic elastic tensor have potential applications for acoustic cloaking, noise insulation, and other special acoustic devices. So it is concerned by scientists. In the review, pentamode materials and their recent progress are introduced. It includes the concept of PMs, acoustic and elastic properties of Bragg scattering PMs, locally resonant PMs, fabrications and measurement methods.
PMs with structures perturbed units not only have excellent fluid properties in the single mode region, but also have the complete phonon bandgap. Therefore, in addition to the use of acoustics clacks, but also can be widely used for vibration and noise reduction, earthquake proof construction, the protection of ancient buildings, design of large concert hall, energy collection and others acoustic devices and so on. The locally resonant PMs proposed by us have the single mode regions and the complete phonon bandgap in the low-frequency regions simultaneously. Compared with the traditional Bragg scattering PMs, the first complete phonon bandgap of locally resonant PMs can be reduced by two orders of magnitude while keeping periodic unit length of structure the same. Locally resonant PMs are a new mechanism different from Bragg scattering PMs. It has excellent low-frequency characteristics and realizes small size (periodic unit length of centimeter scale) to control large wavelength (especially below 100Hz). The locally resonant PMs also have a higher quality factor than the Bragg scattering PMs. Therefore, the locally resonant PMs provide a path to control low-frequency acoustic wave.
Although the acoustic and mechanic properties of PMs have been studied, there are still many characteristics of PMs that need to be studied extensively. It includes the building and design of the novel type PMs, such as low symmetric degree PMs, and different lattice structures PMs; the operating principles of Bragg scatting PMs, locally resonant PMs, and the Snell’s law of the 2D PMs; the methods of fast and high-efficient numerical calculations of PMs, the optimization designs of coding pentamode metamaterials, and the high-precision fabrication technology of PMs.
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图 3 双锥窄直径不同型五模式超材料结构以及当非对称度为0.4时的能带图[21]. (a)双锥窄直径不同型五模式超材料结构示意图. (b) m=d2/d1=0.4时在空气中的能带图.
图 16 材料参数对压缩波相速度、剪切波相速度以及二者相速度比值的影响. (a)密度对相速度以及比值的影响. (b)杨氏模量对相速度以及比值的影响. (c)泊松比对相速度以及比值的影响.
表 1 材料体密度与五模式超材料声学参数的关系
密度
/kg·m-3fl
/kHzfh
/kHzABW
/kHzRBW fmax
/kHzcB/cG 1000 7.35 10.6 3.25 0.362 16.3 15.365 1190 6.74 9.7 2.96 0.36 14.9 15.359 1290 6.48 9.32 2.84 0.359 14.3 15.346 1390 6.24 8.98 2.74 0.36 13.8 15.36 1590 5.83 8.39 2.56 0.36 12.9 15.34 1990 5.21 7.5 2.29 0.361 11.5 15.349 2190 4.97 7.15 2.18 0.36 11 15.35 3500 3.93 5.66 1.73 0.361 8.7 15.37 
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表 2 杨氏模量与五模式超材料声学参数的关系
杨氏模量
/GPafl
/kHzfh
/kHzABW
/kHzRBW fmax
/kHzcB/cG 3 6.74 9.7 2.96 0.36 14.1 15.359 6 9.53 13.7 4.17 0.359 20.0 15.357 10 12.3 17.7 5.4 0.36 25.8 15.36 20 17.4 25.1 7.7 0.363 38.5 15.41 30 21.3 30.7 9.4 0.362 44.7 15.365 40 24.6 35.4 10.8 0.36 51.7 15.357 50 27.5 39.6 12.1 0.361 57.7 15.36 60 30.1 43.4 13.3 0.362 63.3 15.40
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表 3 泊松比与五模式超材料声学参数的关系
泊松比 fl
/kHzfh
/kHzABW
/kHzRBW fmax
/kHzcB/cG 0.1 6.7 9.7 3.0 0.366 15.2 15.42 0.2 6.71 9.7 2.99 0.364 15.2 15.40 0.3 6.72 9.7 2.98 0.363 15.0 15.41 0.4 6.74 9.7 2.96 0.360 14.9 15.36 0.46 6.76 9.71 2.95 0.358 14.9 15.32
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